The uniform Kadec-Klee property for the Lorentz spaces Lw,1
نویسندگان
چکیده
منابع مشابه
THE UNIFORM KADEC-KLEE PROPERTY FOR THE LORENTZ SPACES Lw,1
In this paper we show that the Lorentz space Lw,1(0,∞) has the weak-star uniform Kadec-Klee property if and only if inf t>0 w(αt) w(t) > 1 and sup t>0 φ(αt) φ(t) < 1 for all α ∈ (0, 1),
متن کاملUniform Kadec-Klee Property in Banach Lattices
We prove that a Banach lattice X which does not contain the ln ∞uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology τ on X. In case the Banach lattice is purely atomic, the topology τ is the coordinatewise convergence topology. 1980 Mathematics Subject Classification: Primary 46B03, 46B42.
متن کاملOn Semi-Uniform Kadec-Klee Banach Spaces
and Applied Analysis 3 We now introduce a property lying between U-space and semi-KK. Definition 1.8. We say that a Banach space X is semi-uniform Kadec-Klee if for every ε > 0 there exists a δ > 0 such that semi-UKK : {xn} ⊂ SX xn ⇀ x 〈 xn − x, fn 〉 ≥ ε, for some {fn } ⊂ SX∗ satisfying fn ∈ ∇xn ∀n ⎫ ⎪ ⎪⎬ ⎪ ⎪⎭ ⇒ ‖x‖ ≤ 1 − δ. 1.10 In this paper, we prove that semi-UKK property is a nice generali...
متن کاملBanach Spaces Which Admit a Norm with the Uniform Kadec-klee Property
Several results are established about Banach spaces X which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from X to the Lebesgue-Bochner space L2(X) if and only if X is super-re exive. A basis characterization of the renorming property for dual Banach spaces is g...
متن کاملUNIFORM KADEC-KLEE LORENTZ SPACES Lw,1 AND UNIFORMLY CONCAVE FUNCTIONS
We consider the notion of a uniformly concave function, using it to characterize those Lorentz spaces Lw,1 that have the weak-star uniform Kadec-Klee property as precisely those for which the antiderivative φ of w is uniformly concave; building on recent work of Dilworth and Hsu. We also derive a quite general sufficient condition for a twice-differentiable φ to be uniformly concave; and explor...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1996
ISSN: 0263-6115
DOI: 10.1017/s1446788700037356